What's the exact area and the exact perimeter of square EFGH shown in the coordinate plane?

Using the distance between two points to find the length of the side of the square, it is found that:

The distance between two points and is given by:

In this problem, the length of the side of the square can be found as the distance between points G and H, that is, the distance between (0,5) and (-5,0), hence:

The area of a square of side length l is given by:

Hence:

The area is of 50 square units.

The perimeter of a square of side length l is given by:

Hence:

The perimeter is of units.

You can learn more about distance between two points at link